Sequences That Satisfy a(n-a(n))=0

Abstract:
We explore the properties of some sequences for which
a(n-a(n))=0.
Under the natural restriction that a(n) < n the
number of such sequences is a Bell number. Adding other natural
restrictions yields sequences counted by the Catalan numbers, the
Narayana numbers, the triangle of triangular binomial
coefficients, and the Schröder numbers.